Multiplying Polynomials | Naruhodo Tutoring

Polynomial Inputs

Polynomial 1

Use ^ for exponents: 2x^2 - x + 1

Polynomial 2

Negative terms: use − or -

Examples

Result

Enter two polynomials above, then press Multiply → to see the product with step-by-step work.

FOIL Method

Product

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Degree

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Terms

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Method

FOIL Method for Binomials

(a + b)(c + d) = ac + ad + bc + bd

FOIL is an acronym that helps you remember which terms to multiply when expanding two binomials. Each letter names a pair of terms:

F — First: multiply the first term of each binomial: a · c
O — Outer: multiply the outer terms (first of #1 × last of #2): a · d
I — Inner: multiply the inner terms (last of #1 × first of #2): b · c
L — Last: multiply the last term of each binomial: b · d

FOIL is just a memory aid for the distributive property. It works for any two binomials, but for trinomials or larger you need full distribution.

Special Patterns to Know

Some products appear so often that recognizing their patterns saves time:

(a + b)² = a² + 2ab + b² — perfect square trinomial
(a − b)² = a² − 2ab + b² — perfect square trinomial
(a + b)(a − b) = a² − b² — difference of squares (middle terms cancel)
General: each term of the first polynomial multiplies every term of the second

Tip: enter (x+2)(x+2) or (x+3)(x-3) above to see these patterns in action.

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